# 5.9.3 Collisions

Higher Tier Only

### Collisions

• Examples of momentum in an event are collisions
• Objects will either:
• Collide and move in opposite directions – this is an elastic colision
• Collide and move in the same direction together – this is an inelastic collision
• When the objects move in opposite directions:
• Each object will have a different velocity depending on its mass and initial momentum of the system
• When the objects move in the same direction together:
• They will have a combined mass and velocity
• Momentum is always conserved in a collision Types of collisions

#### Exam Tip

If an exam question asks you to analyse a collision, follow these tips for full marks:

• Always consider the motion before and after the collision and state:
• The velocities of each object
• The direction each object moves
• State whether the collision was elastic or inelastic and explain your reasoning
• In a perfectly elastic collision, the kinetic energy is the same before and after
• In a perfectly inelastic collision, the two objects stick together after colliding
• Describe any energy transfers that occur if kinetic energy is not conserved
• For example, it may be converted into heat, sound, elastic potential energy etc
Higher Tier Only

### Calculations Involving Collisions

• Calculations involving collisions use the conservation of momentum to determine the velocity of an object (or objects) before or after the collision
• This means the momentum before the collision must equal the momentum after the collision for momentum to be conserved

#### Worked Example

An object of mass 1 kg is travelling at 3 m/s when it collides with a heavier object of mass 2 kg. The two objects stick together and travel off as one.

Calculate the combined velocity of the objects after the collision.

Step 1: Draw a diagram Step 2: State the principle of conservation of momentum

The total momentum before a collision = The total momentum after a collision

Step 3: Calculate the momentum before the collision

• Before the collision, only the 1 kg object has any momentum

pbefore = mv = 1 × 3 = 3 kg m/s

Step 3: Determine the momentum after the collision

• The combined mass is now 1 + 2 = 3 kg

pafter = mv = 3 × v

Step 4: Substitute values into conservation equation

pbefore = pafter

3 = 3 × v

Step 5: Rearrange for the combined velocity v

v = 3 ÷ 3 = 1 m/s

#### Exam Tip

Always double-check the signs (positive or negative) for the velocity in your answers, as this is the most common type of calculation error! ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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